BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Wavelet Techniques for Advanced Biomedical Image Reconstruction

M. Unser

Minicourse on Mathematics of Emerging Biomedical Imaging III, Paris, French Republic, February 4-6, 2009.

Our purpose in this talk is to advocate the use of wavelets for image denoising and reconstruction. We start with a short tutorial on wavelet bases, emphasizing the fact that they provide a concise multiresolution representation of images and that they can be computed most efficiently. We then discuss a simple but remarkably effective image-denoising procedure that essentially amounts to discarding small wavelet coefficients (soft-thresholding); we show that this type of algorithm is the solution of a variational problem that promotes sparse solutions. We argue that the underlying principle of wavelet regularization is a powerful concept that can be used advantageously in a variety of inverse image-reconstruction problems. We discuss an elegant iterative solution for general linear inverse problems (Daubechies, Defrise and De Mol, 2004), and present a new multi-level extension this algorithm that yields much faster convergence. We illustrate the concept with several concrete imaging examples: the fast deconvolution of 3-D fluorescence micrographs, the reconstruction of dynamic PET data, and the reconstruction of magnetic resonance images in non-standard configuration (multi-coil system/non- cartesian k-space sampling). 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser0904.html,
AUTHOR="Unser, M.",
TITLE="Wavelet Techniques for Advanced Biomedical Image Reconstruction",
BOOKTITLE="Minicourse on Mathematics of Emerging Biomedical Imaging
	{III}",
YEAR="2009",
editor="",
volume="",
series="",
pages="",
address="Paris, French Republic",
month="February 4-6,",
organization="",
publisher="",
note="")
© 2009 Institut Henri Poincaré. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from Institut Henri Poincaré. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.